Modern Developments in Asymptotic Ray Theory
Lead Research Organisation:
University of Nottingham
Department Name: Sch of Mathematical Sciences
Abstract
Ray methods applied to the Helmholtz equation have been developed for, and applied to, high-frequency diffraction and scattering problems with unparalleled success. This theory underpins mathematical optics and is fundamental to the geometrical theory of diffraction. It relies upon describing waves in terms of an amplitude expansion and a single phase term, from which partial differential equations for these quantities follow.
The lead investigator has identified a novel class of topical problems for which this approach does not work, and the plan is to modify substantially the existing theory by the inclusion of a generalised sum of terms in the phase, and then to apply the newly generalised theory to these problems.
The lead investigator has identified a novel class of topical problems for which this approach does not work, and the plan is to modify substantially the existing theory by the inclusion of a generalised sum of terms in the phase, and then to apply the newly generalised theory to these problems.
Organisations
Publications
Radjen A
(2019)
Reflection and transmission of high-frequency acoustic, electromagnetic and elastic waves at a distinguished class of irregular, curved boundaries
in IMA Journal of Applied Mathematics
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/N50970X/1 | 30/09/2016 | 29/09/2021 | |||
1982197 | Studentship | EP/N50970X/1 | 01/12/2017 | 30/09/2021 | Anthony Radjen |
Description | Classic ray theory can be used to address many of the wave scattering phenomena which occur in many applications of wave theory. This project highlights and treats areas and problems for which classic ray theory is not directly appropriate, and must be modified to suit those problems. A sample of the theory and problems were published in a journal article [1]: [1]: https://academic.oup.com/imamat/article-abstract/84/6/1203/5681665 |
Exploitation Route | The findings of this project have applications in modern wave theory and so can be used, for example, by engineers, especially those working in the area of acoustics and/or electromagnetics. |
Sectors | Aerospace Defence and Marine Electronics Other |
URL | https://academic.oup.com/imamat/article-abstract/84/6/1203/5681665 |